Why is the correct counter for rabbits 羽（わ）, the counter that is used for birds.
I figured it is because they jump, cause fly and jump are the same verb in Japanese, but then frogs are 匹.
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I also heard the Buddhist monk story, but another theory is that while the word ウサギ is theorized to have come to Japanese from a Sanskrit origin through Korea, it was reinterpreted by some as う+鷺, providing a linguistic connection to birds and to the 羽 counter.
The usual story is that Japanese Buddhist monks, who were unable to eat meat other than birds, liked the taste of rabbit so much that they "reclassified" them as flightless birds due to their various body features.
The Sanskrit origin feels most satisfying, but I'll add one more that Wikipedia mentions: hunters would carry their kills by the ears, tying them up and carrying them in bundles. One bundle would be 一把 (いちわ), two 二把...supposedly counting rabbits in this way, わ became associated with 羽.
羽(わ) is used because there is some stories that rabbit live in Moon, but using 匹（ひき）is also not wrong, and even sometimes used 一耳(ひとみみ）.
Jump and Fly both can read as とぶ、but they have different Kanjis 跳ぶ, 飛ぶ. actually, so may be that's not the reason, I think ....